Related papers: Physical States and Transition Amplitudes in Piece…
In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geometries. At the crossroad of topological quantum field theory,…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
We adopt a novel approach to combine path integral methods with Loop Quantum Gravity (LQG). Our approach builds upon the recently developed coherent state path integral formulation of LQG to compute the one-loop effective action. We compare…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Experiments at the interface of quantum field theory and general relativity would greatly benefit theoretical research towards their unification. The gravitational aspects of quantum experiments performed so far can be explained either…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
We construct a coherent state path integral formalism for the one-dimensional Bloch particle within the single band model. The transition amplitude between two coherent states is a sum of transition amplitudes with different winding numbers…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…